Inference for exponential parameter under progressive Type-II censoring from imprecise lifetime

Progressively Type-II censored sampling is an important method ofobtaining data in lifetime studies. Statistical analysis oflifetime distributions under this censoring scheme is based onprecise lifetime data. However, in realsituations all observations and measurements of progressive Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. In this paper, we consider the estimation of exponential meanparameter under progressive Type-II censoring scheme, when thelifetime observations are fuzzy and are assumed to be related tounderlying crisp realization of a random sample. We propose a newmethod to determine the maximum likelihood estimate (MLE) of theunknown mean parameter. In addition, a new numerical method forparameter estimation based on fuzzy data is provided. Using the parametric bootstrapmethod, we then discuss the construction of confidence intervalsfor the mean parameter. Monte Carlo simulations are performed toinvestigate the performance of all the different proposedmethods. Finally, an illustrative example is also included

Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment

Exact Reliability for Consecutive k-out-of-r-from-n: F System with Equal and Unequal Components Probabilities

A consecutive k-out-of-r-from-n: F system consists of n linear ordered components such that the system fails if and only if there exist a set of r consecutive linear component that contains at least k failed components. Consecutive k-out-of-r-from-n: F system has been considered in many fields such as reliability analysis. All recent efforts in this area have been focused on acquiring band or approximation for their reliability such that less attention has been paid to their closed form and exact reliability in the literature. In the present paper, with designing an innovative algorithm the exact reliability for extensive class of consecutive k-out-of-r-from-n: F system is obtained. Specially this task for equal and unequal components probabilities is done. Finally, the numerical results for calculating the exact reliability in extensive class of this strategic systems were applied

Constructing gene regulatory networks from microarray data using non-Gaussian pair-copula Bayesian networks

Many biological and biomedical research areas such as drug design require analyzing the Gene Regulatory Networks (GRNs) to provide clear insight and understanding of the cellular processes in live cells. Under normality assumption for the genes, GRNs can be constructed by assessing the nonzero elements of the inverse covariance matrix. Nevertheless, such techniques are unable to deal with non-normality, multi-modality and heavy tailedness that are commonly seen in current massive genetic data. To relax this limitative constraint, one can apply copula function which is a multivariate cumulative distribution function with uniform marginal distribution. However, since the dependency structures of different pairs of genes in a multivariate problem are very different, the regular multivariate copula will not allow for the construction of an appropriate model. The solution to this problem is using Pair-Copula Constructions (PCCs) which are decompositions of a multivariate density into a cascade of bivariate copula, and therefore, assign different bivariate copula function for each local term. In fact, in this paper, we have constructed inverse covariance matrix based on the use of PCCs when the normality assumption can be moderately or severely violated for capturing a wide range of distributional features and complex dependency structure. To learn the non-Gaussian model for the considered GRN with non-Gaussian genomic data, we apply modified version of copula-based PC algorithm in which normality assumption of marginal densities is dropped. This paper also considers the Dynamic Time Warping (DTW) algorithm to determine the existence of a time delay relation between two genes. Breast cancer is one of the most common diseases in the world where GRN analysis of its subtypes is considerably important; Since by revealing the differences in the GRNs of these subtypes, new therapies and drugs can be found. The findings of our research are used to construct GRNs with high performance, for various subtypes of breast cancer rather than simply using previous models

Approximating non-Gaussian Bayesian networks using minimum information vine model with applications in financial modelling

Many financial modeling applications require to jointly model multiple uncertain quantities to presentmore accurate, near future probabilistic predictions. Informed decision making would certainly benefitfrom such predictions. Bayesian networks (BNs) and copulas are widely used for modeling numerousuncertain scenarios. Copulas, in particular, have attracted more interest due to their nice property ofapproximating the probability distribution of the data with heavy tail. Heavy tail data is frequentlyobserved in financial applications. The standard multivariate copula suffer from serious limitations whichmade them unsuitable for modeling the financial data. An alternative copula model called the pair-copulaconstruction (PCC) model is more flexible and efficient for modeling the complex dependence of finan-cial data. The only restriction of PCC model is the challenge of selecting the best model structure. Thisissue can be tackled by capturing conditional independence using the Bayesian network PCC (BN-PCC).The flexible structure of this model can be derived from conditional independences statements learnedfrom data. Additionally, the difficulty of computing conditional distributions in graphical models for non-Gaussian distributions can be eased using pair-copulas. In this paper, we extend this approach furtherusing the minimum information vine model which results in a more flexible and efficient approach inunderstanding the complex dependence between multiple variables with heavy tail dependence andasymmetric features which appear widely in the financial applications

Gaussian Process emulation of spatiotemporal outputs of a 2D inland flood model

The computational limitations of complex numerical models have led to adoption of statistical emulators across a variety of problems in science and engineering disciplines to circumvent the high computational costs associated with numerical simulations. In flood modelling, many hydraulic and hydrodynamic numerical models, especially when operating at high spatiotemporal resolutions, have prohibitively high computational costs for tasks requiring the instantaneous generation of very large numbers of simulation results. This study examines the appropriateness and robustness of Gaussian Process (GP) models to emulate the results from a hydraulic inundation model. The developed GPs produce real-time predictions based on the simulation output from LISFLOOD-FP numerical model. An efficient dimensionality reduction scheme is developed to tackle the high dimensionality of the output space and is combined with the GPs to investigate the predictive performance of the proposed emulator for estimation of the inundation depth. The developed GP-based framework is capable of robust and straightforward quantification of the uncertainty associated with the predictions, without requiring additional model evaluations and simulations. Further, this study explores the computational advantages of using a GP-based emulator over alternative methodologies such as neural networks, by undertaking a comparative analysis. For the case study data presented in this paper, the GP model was found to accurately reproduce water depths and inundation extent by classification and produce computational speedups of approximately 10,000 times compared with the original simulator, and 80 times for a neural network-based emulator

Probabilistic Modeling of Financial Uncertainties

Since the global financial crash, one of the main trends in the financial engineering discipline has been to enhance the efficiency and flexibility of financial probabilistic risk assessments. Creditors could immensely benefit from such improvements in analysis hoping to minimise potential monetary losses. Analysis of real world financial scenarios require modeling of multiple uncertain quantities with a view to present more accurate, near future probabilistic predictions. Such predictions are essential for an informed decision making. In this paper, we extend Bayesian Networks Pair-Copula Construction (BN-PCC) further using the minimum information vine model which results in a more flexible and efficient approach in modeling multivariate dependencies of heavy-tailed distribution and tail dependence as observed in the financial data. We demonstrate that the extended model based on minimum information Pair-Copula Construction (PCC) can approximate any non-Gaussian BN to any degree of approximation. Our proposed method has been applied to the portfolio data derived from a Brazilian case study. The results show that the fitting of the multivariate distribution approximated using the proposed model has been improved compared to other previously published approaches